Dadas las coordenadas del centro de una esfera (cx, cy, cz) y su radio r . Nuestra tarea es comprobar si un punto (x, y, z) se encuentra dentro, fuera o sobre esta esfera.
Ejemplos:
Input : Centre(0, 0, 0) Radius 3
Point(1, 1, 1)
Output :Point is inside the sphere
Input :Centre(0, 0, 0) Radius 3
Point(2, 1, 2)
Output :Point lies on the sphere
Input :Centre(0, 0, 0) Radius 3
Point(10, 10, 10)
Output :Point is outside the sphere
Aproximación:
Si un punto se encuentra dentro de una esfera o no, depende de su distancia al centro.
Un punto (x, y, z) está dentro de la esfera con centro (cx, cy, cz) y radio r si
( x-cx ) ^2 + (y-cy) ^2 + (z-cz) ^ 2 < r^2
Un punto (x, y, z) se encuentra en la esfera con centro (cx, cy, cz) y radio r si
( x-cx ) ^2 + (y-cy) ^2 + (z-cz) ^ 2 = r^2
Un punto (x, y, z) está fuera de la esfera con centro (cx, cy, cz) y radio r si
( x-cx ) ^2 + (y-cy) ^2 + (z-cz) ^ 2 > r^2
C++
// CPP code to illustrate above approach
#include <bits/stdc++.h>
using namespace std;
// function to calculate the distance between centre and the point
int check(int cx, int cy, int cz, int x, int y, int z)
{
int x1 = pow((x - cx), 2);
int y1 = pow((y - cy), 2);
int z1 = pow((z - cz), 2);
// distance between the centre
// and given point
return (x1 + y1 + z1);
}
// Driver program to test above function
int main()
{
// coordinates of centre
int cx = 1, cy = 2, cz = 3;
int r = 5; // radius of the sphere
int x = 4, y = 5, z = 2; // coordinates of point
int ans = check(cx, cy, cz, x, y, z);
// distance btw centre and point is less
// than radius
if (ans < (r * r))
cout << "Point is inside the sphere";
// distance btw centre and point is
// equal to radius
else if (ans == (r * r))
cout << "Point lies on the sphere";
// distance btw center and point is
// greater than radius
else
cout << "Point is outside the sphere";
return 0;
}
Java
// Java code to illustrate above approach
import java.io.*;
import java.util.*;
import java.lang.*;
class GfG {
// function to calculate the distance
// between centre and the point
public static int check(int cx, int cy,
int cz, int x, int y, int z)
{
int x1 = (int)Math.pow((x - cx), 2);
int y1 = (int)Math.pow((y - cy), 2);
int z1 = (int)Math.pow((z - cz), 2);
// distance between the centre
// and given point
return (x1 + y1 + z1);
}
// Driver program to test above function
public static void main(String[] args)
{
// coordinates of centre
int cx = 1, cy = 2, cz = 3;
int r = 5; // radius of the sphere
// coordinates of point
int x = 4, y = 5, z = 2;
int ans = check(cx, cy, cz, x, y, z);
// distance btw centre and point is less
// than radius
if (ans < (r * r))
System.out.println("Point is inside"
+ " the sphere");
// distance btw centre and point is
// equal to radius
else if (ans == (r * r))
System.out.println("Point lies on"
+ " the sphere");
// distance btw center and point is
// greater than radius
else
System.out.println("Point is outside"
+ " the sphere");
}
}
// This code is contributed by Sagar Shukla.
Python
# Python3 code to illustrate above approach
import math
# function to calculate distance btw center and given point
def check(cx, cy, cz, x, y, z, ):
x1 = math.pow((x-cx), 2)
y1 = math.pow((y-cy), 2)
z1 = math.pow((z-cz), 2)
return (x1 + y1 + z1) # distance between the centre and given point
# driver code
cx = 1
cy = 2 # coordinates of centre
cz = 3
r = 5 # radius of sphere
x = 4
y = 5 # coordinates of the given point
z = 2
# function call to calculate distance btw centre and given point
ans = check(cx, cy, cz, x, y, z);
# distance btw centre and point is less than radius
if ans<(r**2):
print("Point is inside the sphere")
# distance btw centre and point is equal to radius
elif ans ==(r**2):
print("Point lies on the sphere")
# distance btw centre and point is greater than radius
else:
print("Point is outside the sphere")
C#
// C# code to illustrate
// above approach
using System;
class GFG
{
// function to calculate
// the distance between
// centre and the point
public static int check(int cx, int cy,
int cz, int x,
int y, int z)
{
int x1 = (int)Math.Pow((x - cx), 2);
int y1 = (int)Math.Pow((y - cy), 2);
int z1 = (int)Math.Pow((z - cz), 2);
// distance between the
// centre and given point
return (x1 + y1 + z1);
}
// Driver Code
public static void Main()
{
// coordinates of centre
int cx = 1, cy = 2, cz = 3;
int r = 5; // radius of the sphere
// coordinates of point
int x = 4, y = 5, z = 2;
int ans = check(cx, cy, cz,
x, y, z);
// distance btw centre
// and point is less
// than radius
if (ans < (r * r))
Console.WriteLine("Point is inside" +
" the sphere");
// distance btw centre
// and point is
// equal to radius
else if (ans == (r * r))
Console.WriteLine("Point lies on" +
" the sphere");
// distance btw center
// and point is greater
// than radius
else
Console.WriteLine("Point is outside" +
" the sphere");
}
}
// This code is contributed by anuj_67.
PHP
<?php
// function to calculate
// the distance between
// centre and the point
function check($cx, $cy, $cz,
$x, $y, $z)
{
$x1 = pow(($x - $cx), 2);
$y1 = pow(($y - $cy), 2);
$z1 = pow(($z - $cz), 2);
// distance between the
// centre and given point
return ($x1 + $y1 + $z1);
}
// Driver Code
// coordinates of centre
$cx = 1;
$cy = 2;
$cz = 3;
$r = 5; // radius of the sphere
$x = 4;
$y = 5;
$z = 2; // coordinates of point
$ans = check($cx, $cy, $cz,
$x, $y, $z);
// distance btw centre and
// point is less than radius
if ($ans < ($r * $r))
echo "Point is inside " .
"the sphere";
// distance btw centre and
// point is equal to radius
else if ($ans == ($r * $r))
echo "Point lies on the sphere";
// distance btw center and point
// is greater than radius
else
echo "Point is outside " .
"the sphere";
// This code is contributed
// by shiv_bhakt
?>
Javascript
<script>
// Javascript code to illustrate above approach
// function to calculate the distance between centre and the point
function check(cx, cy, cz, x, y, z)
{
let x1 = Math.pow((x - cx), 2);
let y1 = Math.pow((y - cy), 2);
let z1 = Math.pow((z - cz), 2);
// distance between the centre
// and given point
return (x1 + y1 + z1);
}
// Driver program to test above function
// coordinates of centre
let cx = 1, cy = 2, cz = 3;
let r = 5; // radius of the sphere
let x = 4, y = 5, z = 2; // coordinates of point
let ans = check(cx, cy, cz, x, y, z);
// distance btw centre and point is less
// than radius
if (ans < (r * r))
document.write("Point is inside the sphere");
// distance btw centre and point is
// equal to radius
else if (ans == (r * r))
document.write("Point lies on the sphere");
// distance btw center and point is
// greater than radius
else
document.write("Point is outside the sphere");
// This code is contributed by Mayank Tyagi
</script>
Producción:
Point is inside the sphere
Complejidad de tiempo: O(1)